The Traitors and rational choice
How did it all go so right?
If you haven’t seen the last episode of The Traitors (UK) series two, don’t read this as it contains spoilers galore. If you don’t watch The Traitors at all, you’ll need no encouragement from me not to read this, but you should watch it because it’s amazing TV and is all about how people respond to economic incentives. Last night’s episode should be used to teach game theory.
If you’ve got this far, you’ll know that Harry won after Jas forced another banishment when only three contestants remained. Many people have been saying that once Jas voted for another banishment, it should have been obvious to Mollie that Jas was a faithful and therefore she was irrational to vote him out. This is pretty much true and it turned out to be true, but there are a few nuances worth considering.
Mollie knows she is a faithful. From her point of view, Jas could only have forced another banishment for one of the following reasons:
Jas is a faithful and thinks that Harry is a traitor, but he’s wrong.
Jas is a faithful and thinks that Harry is a traitor, and he’s right.
They’re all faithfuls but Jas wants to split the pot two ways instead of three.
Jas and Harry are both traitors and Jas wants all the money for himself.
If 4 is correct, Mollie is screwed whatever she does. A traitor is getting the money and she’s going home with nothing. Therefore it makes no difference who she votes for.
If 3 is correct, Jas is playing a very dangerous game because he knows that Mollie trusts Harry more than him. A third of the pot is a lot better than nothing. Would he really risk losing £30,000 for a long odds bet on winning an extra £20,000? It seems extremely unlikely. (Incidentally, the fact that Jas did indeed take this gamble suggests that he was very confident that Harry was a traitor. He must have judged that his chances of surviving the vote were higher than the chances of Harry being a faithful, which they were. Or he was very confident that Mollie would respond to the signals with perfect rationality, which she didn’t.)
If 1 or 2 are correct, she has to vote for Harry because, unless Jas has suddenly become irrational to the point of insanity, Harry is the only person who could possibly be a traitor. She might genuinely believe that neither of them are traitors but since she has to vote for someone, she shouldn’t vote for the person who has essentially proven that he is a faithful.
Mollie may have felt 100% certain that neither of them were traitors and so decided to punish Jas for taking money from a loyal comrade at the eleventh hour. I wouldn’t be surprised if this crossed her mind, but she couldn’t be 100% certain about Harry whereas, if we discount 3 as being vanishingly unlikely, Jas was clearly a faithful.
There is one more possibility worth considering, although it is so unlikely as to be almost theoretical. Let’s imagine that Jas is the final traitor. Once they had banished Andrew and were down to three, Jas may have expected Mollie and Harry to vote for one more banishment. If they voted to banish and he voted to end the game, he would look like the traitor. Therefore he voted to banish and ride his luck. This never looked likely and I doubt the thought occurred to Mollie, but I mention it because it is one of the only ways in which Jas’s decision to banish again would be consistent with him being a traitor.
In conclusion, the criticism that Mollie was irrational and let her heart rule her head is basically correct. Jas’s vote for one last banishment does not completely rule him out as a traitor, but there are only two reasons why a traitor would do that and both of them are so unlikely that the possibility should have been considered extremely remote.
Harry came very, very close to losing and I think this highlights one of the flaws of the game. In the first series, the team found themselves in a situation in which the only economically rational move was to vote Will out, even though they didn’t really think he was a traitor. Homo economicus won the day and Will lost. It turned out to be a good call for the faithful but it was hardly the result of rigorous analysis and well founded suspicions. The same thing very nearly happened this year which, in my view, would have been unfair on Harry who was an exceptionally good player.
The odds seem stacked against the traitors.1 This is partly because traitors get away with leaving very heavy hints against fellow traitors when they get evicted (especially in series one) but also because contestants have an incentive to keep voting people out. The more people who get kicked out, the bigger slice of the pie each contestant gets when they win. This gives them an incentive to banish people for any reason or none for as long as possible (hardly the behaviour you associate with being ‘faithful’). The game could, perhaps, be improved either by cutting the prize fund every time a faithful gets evicted or by having a prize fund for each player rather than for the whole team.
None of this applies to the last episode, however. Jas was right and Mollie was irrational to vote him out.
Someone said on Twitter that the traitors usually win in the US/Australian versions. I don’t know if this is true but I intend to watch them so please don’t leave any spoilers in the comments.
I agree wholeheartedly with your analysis; indeed it is exactly what was being discussed in my own household. The moment Jas initiated a further banishment, it should have been obvious to Mollie that he was a Faithful. Logic dictated that it would have been foolhardy in the extreme, for Jas to have done this, had he been a Traitor. She simply didn't process her thoughts objectively.
She reacted as we feared she might and Harry almost certainly knew she would, to wit: emotionally. I believe that she was enamoured of Will and followed her heart instead of her head.
Jas was in an impossible bind. He could only have played the hand that he did. Mollie let him and herself down. Notwithstanding that Harry took the money, in my opinion the real victor was Jas because Harry was gifted the prize fund by Mollie. Jas didn't lose it, he was failed by a fellow Faithful. He walks away with his self respect, a well earned reputation for being an analytical thinker and his head held high.
In contrast Mollie will always be remembered as..........
It does seem very important to be likeable - the eliminations of Jas and Evie seemed based on female infighting to me, and getting another person eliminated and not seriously thinking about who knocked off Zack. I think Andrew made a mistake murdering Zack, who was starting to get annoying and would have been turned on soon enough.
Good Saturday night in was that, watching the last 3 episodes and then reading this, thanks.